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Journal article
Ergodicity in randomly forced Rayleigh-Benard convection
Nonlinearity, v 29(11), pp 3309-3345
01 Nov 2016
Abstract
We consider the Boussinesq approximation for Rayleigh-Benard convection perturbed by an additive noise and with boundary conditions corresponding to heating from below. In two space dimensions, with sufficient stochastic forcing in the temperature component and large Prandtl number Pr > 0, we establish the existence of a unique ergodic invariant measure. In three space dimensions, we prove the existence of a statistically invariant state, and establish unique ergodicity for the infinite Prandtl Boussinesq system. Throughout this work we provide streamlined proofs of unique ergodicity which invoke an asymptotic coupling argument, a delicate usage of the maximum principle, and exponential martingale inequalities. Lastly, we show that the background method of Constantin and Doering (1996 Nonlinearity 9 1049-60) can be applied in our stochastic setting, and prove bounds on the Nusselt number relative to the unique invariant measure.
Metrics
Details
- Title
- Ergodicity in randomly forced Rayleigh-Benard convection
- Creators
- J. Foldes - University of VirginiaN. E. Glatt-Holtz - Tulane UniversityG. Richards - Utah State UniversityJ. P. Whitehead - Brigham Young University
- Publication Details
- Nonlinearity, v 29(11), pp 3309-3345
- Publisher
- Iop Publishing Ltd
- Number of pages
- 37
- Grant note
- 0932078000; NSF-DMS-1313272 / National Science Foundation; National Science Foundation (NSF) 1440415 / Direct For Mathematical & Physical Scien; National Science Foundation (NSF); NSF - Directorate for Mathematical & Physical Sciences (MPS)
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Physics
- Web of Science ID
- WOS:000384132300002
- Scopus ID
- 2-s2.0-84992343529
- Other Identifier
- 991021869041604721
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Data related to this publication, from InCites Benchmarking & Analytics tool:
- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics, Applied
- Physics, Mathematical